These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
The board game:
Goddamn Bats: The 2-peg PT boat is this. Its small profile allows a lucky player to turn around the entire game even if they're at a disadvantage. Conversely, managing to sink the thing early on makes winning a whole lot easier.
Alternate Character Interpretation: The aliens as a peaceful expedition. They repeatedly avoid harming non-threatening humans and only fire when fired upon, which raises the possibility that they were not invaders or scouting for an attack but peaceful, and twitchy humans botched first contact.
Alex as an arrogant screwup that got lucky throughout the film. That this fits well with his early film portrayal makes it even easier.
Critical Research Failure: The use of Fortunate Son, a explicitly anti-war Vietnam era song, in a very military centric movie.
Fridge Horror: So yeah, the day is saved, but think about it. This is an organized military invading Earth, that lost its means of communication. Sooner or later search and rescue parties are going to be sent, and as soon as they get word out about us...
Fridge Logic: Wait, how did they get the Missouri fueled, loaded, and generally back into fighting condition in only a few hours?
Germans Love David Hasselhoff: Battleship notably made over $200 million overseas before opening in the US. While the film was largely ignored in America, European markets such as the UK helped it make four times more overseas than it did in the US. This might be because the movie had an Audience-Alienating Premise for Americans: it was based on a board game, and the sheer absurdity of making a movie out of a plotless toy made Americans turn away in droves before it even came out. Outside of the USA, the original "Battleship" board game is either unknown or is known by a different name, so overseas audiences were more easily able to view the movie at face value.
Is this the first time that a movie's very existence, even on the most basic conceptual level, been so narmy?
The scene with the veterans stepping up to help prepare and launch the Missouri again, especially when aged veterans in an ancient ship dramatically outperform modern vessels against the aliens. Goes straight into Narm Charm for some.
Narm Charm: Don't take it too seriously and you might just have some fun
Nightmare Fuel: The shots of the interior of the Samson taking on water after being hit by the aliens' weaponry, which includes sailors yelling for help as the compartments they're in start to fill up.
Tear Jerker: Stone's death. Made even worse when you remember that the last thing Alex said to him was "I'm sorry I let you down." And the last shot of him is standing on the ship's deck, scanning the seas for Alex.
What The Hell Casting Agency: Even though her acting was fairly decent, why the hell was Rihanna in this film? (Answer: The director saw an interview and her hosting of SNL and was sufficiently impressed.)